In the News (Tue 20 Mar 18)

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The ambiguity is that "formallogic" is very often used with the alternate meaning of symbolic logic as we have defined it, with informallogic meaning any logical investigation that does not involve symbolic abstraction; it is this sense of 'formal' that is parallel to the received usages coming from "formal languages" or "formal theory".

Relevance logic and paraconsistentlogic are the most important approaches here, though the concerns are different: a key consequence of classicallogic and some of its rivals, such as intuitionisticlogic, is that they respect the principle of explosion, which means that the logic collapses if it is capable of deriving a contradiction.

Logic gates are primarily implemented electronically using diodes or transistors, but can also be constructed using electromagnetic relays, fluidics, optical or even mechanical elements.

Logic circuits are often classified in two groups: combinatorial logic, in which the outputs are continuous-time functions of the inputs, and sequential logic, in which the outputs depend on information stored by the circuits as well as on the inputs.

The field-programmable nature of programmable logic devices such as FPGAs has removed the 'hard' property of hardware; it is now possible to change the logic design of a hardware system by reprogramming some of its components, thus allowing the features or function of a hardware implementation of a logic system to be changed.

In essentials, it is still the logic of Aristotle, but from the point of view of notation it is written as a branch of abstractalgebra.

Attempts to treat the operations of formallogic in a symbolic or algebraic way were made by some of the more philosophical mathematicians, such as Leibniz and Lambert; but their labors remained little known and isolated.

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Technically CL is a game logic: it understands interactive computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems.

The inherent incompleteness of affine or linear logics, resulting from the fundamental limitations of the underlying sequent-calculus approach, is apparently the reason why such intuitions and examples, while so heavily relied on in the popular linear-logic literature, have never really found a good explication in the form of a mathematically strict and intuitively convincing semantics.

Logically, we can use these symbols or we can equate them with others according to the needs of the moment.

One essential reason for basing logical operations on the binary number system is that it is easy to design simple, stable electronic circuits that can switch back and forth between two clearly-defined states, with no ambiguity attached.

Digital logic may be divided into two classes: combinational logic, in which the logical outputs are determined by the logical function being performed and the logical input states at that particular moment; and sequential logic, in which the outputs also depend on the prior states of those outputs.

Professor Matthew Yen's research is focused on the application of "fuzzylogic" in the control of equipment such as heaters, motors, pumps, valves and sprinklers used in the food processing industry and other automated agricultural operations.

Generally speaking, the procedures of fuzzylogic control are these: A set of input data from an array of sensors is fed into the control system.

Besides temperature controls, fuzzylogic has been implemented or proposed for many other processes in food technology, namely aseptic processing; diagnosis of principle causes of breakage during drying; determination of key ingredients for new products; evaluation of the "doneness" of beef steak; intelligent irrigation; automated feeding systems; and so on.

The rise of modernformallogic following the work of Frege and Russell brought with it a recognition of the many serious limitations of Aristotle'slogic; today, very few would try to maintain that it is adequate as a basis for understanding science, mathematics, or even everyday reasoning.

The MSc in Logic is a highly interdisciplinary and international two-year research Master's degree that has been in existence since 1995.

The goal of the ILLC (and as such the underlying spirit of the MSc in Logic) is to connect the traditional fundamental research in the formal sciences with a broad range of applications from information sciences to linguistics and philosophy.

All students follow a historical introduction into modern research in logic in the course Core Logic which is obligatory for all students.

Charles Peirce's contributions to logicaltheory are numerous and profound.

It has been frequently claimed that real progress in logic was only realized in the work of Frege and later work of Peirce in which the equational paradigm was dropped and the powerful expressive ability of quantification theory was realized.

Following his development of quantification theory, Peirce developed a graphical system for analyzing logicalreasoning that he felt was superior in analytical power to his algebraic and quantificational notations.